I have always had a fascination with the Courageous class batlecruisers of The first world war.Basically a Light Cruiser with a battleships armament, designed to take the fight to Germany's Baltic coast.

HMS Furious was the first to be converted into a carrier, in fact, Furious never had the second of it's 18" guns mounted, having a half a flight deck instead. That was in 1916.

Courageous and Glorious where nearly scrapped at the end of the war, but they followed their sister's path instead: conversion into an Aircraft Carrier.
During the second world war, as you all know, Courageous and Glorious where lost early on, but what if they just weren't there?
What if they where scrapped at the end of the first world war?
Maybe it would have been Furious sunk by Scharnhorst and Gneisensau?

Or would Britain be able to afford building some new carriers from scratch; or would Ark Royal have a few sisters?

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It is very likely that Britain would have built two more carriers of about the same size as Ark Royal but without two full hanger decks to reach their allowable tonnage under the Washington Naval Treaty. They might also have converted one or two other ships for this purpose instead.
Britain historically built right to the limit of their allowable carrier tonnage. I see no reason they would not have done so in this scenario either. But, much of Britain's carrier tonnage historically was conversions of other vessels to carriers that resulted in the odd polyglot of ships they started WW 2 with. Given financial constraints and the lack of a really strong FAA and good aircraft it is likely that Britain would still try to build carriers on a shoestring rather than turn out properly designed ones.

I agree. Despite the Royal Navy's early lead in aircraft carrier experiments, there was never the level of commitment to aircraft carrier development that characterized the USN and IJN. Until the outbreak of WW II, the RN gave higher priority to building other ship types, which, given the dominance of the strategic bombardment types in British military aviation circles, and the relative weakness of naval aviation, was completely understandable.

This question leads towards the WI: the RN takes a broader approach to a fleet air arm and instead of the smaller conversions aims for larger size carriers and much more capable aircraft. To make much of difference I suspose the changes would have to reach back into the early 1920s, particularly for the R&D of better aircraft.

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The problem there (the FAA) is the RAF. There were limited funds for each service. The RAF wanted control of all aircraft, both on land and at sea. The RN was loath to give the RAF control. Given the limited funding available, the RN ran a compromise whereby they would have effective control of the FAA but the RAF would be the service providing the funds and aircraft.
Typical of most compromises it gave the RN the worst of both worlds. In this case few and poor aircraft as the RAF's priorities lay elsewhere.

So the line of speculation leads to no compromise & the RN has control of its own R & D. A quick glance at the aircraft types avaialble in the 1930s turns up nothing impressive. Not much to base speculation on.

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